Limiting electrophoretic mobility of a highly charged soft particle in an electrolyte solution: Solidification effect

It is known that the electrophoretic mobility of a spherical rigid particle in an electrolyte solution with large κa (where κ = Debye–Hückel parameter and a = particle radius) and large Dukhin number (Du ≫ 1) tends to a nonzero constant value in the limit of high zeta potentials. A highly charged liquid drop exhibits the same limiting mobility value. That is, a liquid drop behaves as if it were a rigid particle (the solidification effect). In the present paper we derive the corresponding mobility expression for a highly charged spherical soft particle (i.e., a polyelectrolyte-coated particle) consisting of the particle core of radius a covered with an ion-penetrable surface layer of thickness d in a symmetrical electrolyte solution of valence z. It is shown that for κa ≫ and κd ≫ 1, the magnitude of the scaled limiting mobility μ(∞) is given by |μ(∞)| = 2εrεokT/3ηze · (1 + a3/2b3) · 2 ln 2, where εr is the relative permittivity of the electrolyte solution, εo is the permittivity of a vacuum, e is the elementary electric charge, and kT is the thermal energy. When a ≈ b, the obtained limiting mobility expression tends to the result for a rigid sphere. That is, the solidification effect is observed also for a soft particle.

Graphical abstractA soft particle in an external electric field.Figure optionsDownload full-size imageDownload high-quality image (93 K)Download as PowerPoint slideResearch highlights► The limiting electrophoretic mobility of a highly charged soft particle is obtained. ► A highly charged soft particle behaves as if it were a hard particle in the limit of high Donnan potentials. ► A solidification effect is observed for soft particles.